Question

The radii of two right
circular
cylinders are in
the
ratio 3:2
and their height are in ratio of 5:3
find the ratio of their curved surface area​

Answer 1

Step-by-step explanation:

The ratio of the radii of two cylinders is 3:2

Radius of first cylinder (r₁) = 3r

Radius of be second cylinder (r₂)= 2r

The ratio of the heights is 5:3

Height of first cylinder (h₁) = 5h

Height of second cylinder (h₂) = 3h

The curved surface area (CSA) of the cylinder = 2πrh

CSA of 1st cylinder

= 2π r₁ h₁

= 2 × π × 3r × 5h

= 30πrh

CSA of 2nd cylinder

= 2π r₂ h₂

= 2 × π × 2r × 3h

= 12πrh

The ratio of the CSA of two cylinders

= $\sf \dfrac{30\pi rh}{12\pi rh}$

= $\sf \dfrac{30}{12}$

= $\sf \dfrac{5}{2}$

Therefore:-

The ratio of their curved surface area is 5 : 2

Answer 2

Step-by-step explanation:

The ratio of the radii of two cylinders is 3:2

Radius of first cylinder (r₁) = 3r

Radius of be second cylinder (r₂)= 2r

The ratio of the heights is 5:3

Height of first cylinder (h₁) = 5h

Height of second cylinder (h₂) = 3h

The curved surface area (CSA) of the cylinder = 2πrh

CSA of 1st cylinder

= 2π r₁ h₁

= 2 × π × 3r × 5h

= 30πrh

CSA of 2nd cylinder

= 2π r₂ h₂

= 2 × π × 2r × 3h

= 12πrh

The ratio of the CSA of two cylinders

$= \sf \dfrac{30\pi rh}{12\pi rh}$

$= \sf \dfrac{30}{12}$

$= \sf \dfrac{5}{2}$

Therefore:-

The ratio of their curved surface area is 5 : 2